What is log_{10}(x/(y^3z)) ?

The solution to log_{10}(x/(y^3z)) is log_{10}(x)-3log_{10}(y)-log_{10}(z)

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simplify log_{10}(x/(y^3z))

simplify

lo g_{10} (\frac{x}{y ^{3} z})

lo g_{10} (x) - 3 lo g_{10} (y) - lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x}{y ^{3} z})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{x}{y ^{3} z}) = lo g_{10} (x) - lo g_{10} (y^{3} z)

= lo g_{10} (x) - lo g_{10} (y^{3} z)

Simplify

lo g_{10} (y^{3} z) : 3 lo g_{10} (y) + lo g_{10} (z)

= lo g_{10} (x) - (3 lo g_{10} (y) + lo g_{10} (z))

Apply the distributive law:

- (a + b) = - a - b

- (3 lo g_{10} (y) + lo g_{10} (z)) = - 3 lo g_{10} (y) - lo g_{10} (z)

= lo g_{10} (x) - 3 lo g_{10} (y) - lo g_{10} (z)

lo g_{5} (x y)

ln (\frac{x}{6})

lo g_{10} (\frac{10}{x})

ln (\frac{x ^{\frac{1}{2}}}{x ^{2} 1 + x ^{2}})

\frac{1}{2} ln (3 x - 5 y) - ln (4 x + y)

What is log_{10}(x/(y^3z)) ?
The solution to log_{10}(x/(y^3z)) is log_{10}(x)-3log_{10}(y)-log_{10}(z)